I grew desperate, eating a bug (6)
I believe the answer is:
earwig
'bug' is the definition.
(I've seen this before)
'i grew desperate eating a' is the wordplay.
'desperate' indicates an anagram (a desperate or pathetic spelling).
'eating' means one lot of letters goes inside another.
'i'+'grew'='igrew'
'igrew' anagrammed gives 'erwig'.
'erwig' placed around 'a' is 'EARWIG'.
(Other definitions for earwig that I've seen before include "An insect; to eavesdrop (slang)" , "flatterer" , "Clawed insect" , "Close acquaintance" , "Insect with pincer-like tail" .)